Real gas molecules attract each other and take up space. Johannes van der Waals added two corrections to the ideal gas law in 1873 – a for attraction and b for molecular volume – earning a Nobel Prize and explaining condensation.
How to use the Van der Waals Equation Calculator
- Gas
- a (Pa·m⁶/mol²)
- b (m³/mol)
- Find
- Amount n (mol)
- Volume V
- Temperature T
- Pressure p
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the gas (or enter a and b), what to find, and the amount, volume and temperature or pressure.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Gas | Choose one: Helium, Neon, Hydrogen, Nitrogen … |
| a (Pa·m⁶/mol²) | A number |
| b (m³/mol) | A number |
| Find | Choose one: Pressure p, Temperature T |
| Amount n (mol) | A number |
| Volume V | Units: L, m³, mL, ft³ |
| Temperature T | Units: K, °C, °F |
| Pressure p | Units: kPa, Pa, bar, atm, psi, MPa |
What each result means
- Pressure (van der Waals) = [Amount n (mol)]×8.314462618×[Temperature T]÷([Volume V] – [Amount n (mol)]×[b]) – [a]×[Amount n (mol)]^2÷[Volume V]^2
- Pressure (ideal gas) = [Amount n (mol)]×8.314462618×[Temperature T]÷[Volume V]
- Temperature (van der Waals) = ([Pressure p] + [a]×[Amount n (mol)]^2÷[Volume V]^2)×([Volume V] – [Amount n (mol)]×[b])÷([Amount n (mol)]×8.314462618)
- Temperature (ideal gas) = [Pressure p]×[Volume V]÷([Amount n (mol)]×8.314462618)
Example values
How the main result changes when a changes and everything else stays at the example values above:
| a (Pa·m⁶/mol²) | Pressure (van der Waals) (kPa) |
|---|---|
| 0.0685 | 2,241.5162 |
| 0.1028 | 2,241.5162 |
| 0.137 | 2,241.5162 |
| 0.1713 | 2,241.5162 |
| 0.2055 | 2,241.5162 |
| 0.274 | 2,241.5162 |
Formula
(p + a·n²/V²)·(V − n·b) = n·R·TWorked example
Inputs — Gas: Carbon dioxide; Find: Pressure p; Amount n (mol): 1; Volume V: 1 L; Temperature T: 300 K.
Results — Pressure (van der Waals) = 2,241.51616 kPa; Pressure (ideal gas) = 2,494.33879 kPa.
Key terms
- Real gas
- Gas with intermolecular forces and finite molecular size.
Frequently asked questions
What do a and b represent?
a: intermolecular attraction; b: volume excluded by the molecules.
When is the correction important?
At high pressures and low temperatures.
Can the equation predict condensation?
Qualitatively, with the Maxwell construction.
Is it the most accurate real-gas model?
No – Peng–Robinson and others are better for engineering.